We examine the left-right asymmetry in the cleaned COBE/DIKBE near-infrared data of the inner Galaxy and show (i) that the Galactic bar is probably not seen very nearly end-on, and (ii) that, even if it is, it is not highly elongated. The assumption of constant mass-to-light ratio is used to derive simulated terminal velocity plots for the ISM from our model luminosity distributions. By comparing these plots with observed terminal velocities, we determine the mass-to-light ratio of the near-infrared bulge and disc. Assuming that all this mass contributes to gravitational microlensing, we compute optical depths τ for microlensing in Galactic Centre fields. For three models with bar major axis between 10° and 25° from the Sun-Galactic Centre line, the resulting optical depths in Baade's window lie in the range 0.83 x 10−6 ⋦ τ⋦ s 0.89 x 10−6 for main-sequence stars and 1.2 x 10−6 ⋦ τ ⋦ 1.3 x 10−6 for red clump giants. We discuss a number of uncertainties, including possible variations of the near-infrared mass-to-light ratio. We conclude that, although the values predicted from analysing the COBE and gas velocity data are inconsistent at the 2 — 2.5a level with recent observational determinations of τ, we believe that they should be taken seriously